library(broom)
package ‘broom’ was built under R version 3.6.2
computer <- read_csv(here("data/computers.csv"))

computer <- computer %>%
  unite(price, c(price, X1), sep = ":") 
computer_scale <- computer %>%
  select(hd, ram, price) %>%
  mutate_if(is.numeric, scale) %>%
  column_to_rownames("price")

computer_scale %>%
  ggplot(aes(x = hd, y = ram)) +
  geom_point() 

Some points are very concentrate special in the ram lower to 0, so probably it will work but some cluster we will have more points that others

fviz_nbclust(computer_scale, kmeans, method = "wss", nstart = 25)
Registered S3 method overwritten by 'data.table':
  method           from
  print.data.table     

With Elbow method K means of 3 or 4 look acceptable

fviz_nbclust(computer_scale, kmeans, method = "silhouette", nstart = 25)

Silhouette coefficient proupose k means of 10

fviz_nbclust(computer_scale, kmeans, method = "gap_stat", nstart = 25, k.max = 12)
Clustering k = 1,2,..., K.max (= 12): .. done
Bootstrapping, b = 1,2,..., B (= 100)  [one "." per sample]:
Quick-TRANSfer stage steps exceeded maximum (= 312950)did not converge in 10 iterationsdid not converge in 10 iterations
.
did not converge in 10 iterationsQuick-TRANSfer stage steps exceeded maximum (= 312950)did not converge in 10 iterations
..
did not converge in 10 iterations
..
did not converge in 10 iterations
...
did not converge in 10 iterationsdid not converge in 10 iterations
.
did not converge in 10 iterationsQuick-TRANSfer stage steps exceeded maximum (= 312950)
....
did not converge in 10 iterations
.
did not converge in 10 iterations
..
did not converge in 10 iterationsdid not converge in 10 iterations
.
did not converge in 10 iterationsdid not converge in 10 iterationsdid not converge in 10 iterationsdid not converge in 10 iterationsdid not converge in 10 iterationsdid not converge in 10 iterations
..
did not converge in 10 iterations
.
did not converge in 10 iterations
.
did not converge in 10 iterationsdid not converge in 10 iterations
.
did not converge in 10 iterations
.
did not converge in 10 iterations
.
did not converge in 10 iterations
.
did not converge in 10 iterations
.
did not converge in 10 iterations
.
Quick-TRANSfer stage steps exceeded maximum (= 312950)did not converge in 10 iterations
..
did not converge in 10 iterations
..
did not converge in 10 iterations
.
did not converge in 10 iterationsdid not converge in 10 iterations
...
did not converge in 10 iterations
.
Quick-TRANSfer stage steps exceeded maximum (= 312950)Quick-TRANSfer stage steps exceeded maximum (= 312950)Quick-TRANSfer stage steps exceeded maximum (= 312950)did not converge in 10 iterations
.
did not converge in 10 iterations
..
did not converge in 10 iterations
.
did not converge in 10 iterations
...
did not converge in 10 iterations
.
did not converge in 10 iterationsQuick-TRANSfer stage steps exceeded maximum (= 312950)did not converge in 10 iterations
.
Quick-TRANSfer stage steps exceeded maximum (= 312950)
...
did not converge in 10 iterations
.
did not converge in 10 iterations
. 50 
.....
did not converge in 10 iterationsdid not converge in 10 iterations
.
did not converge in 10 iterations
..
did not converge in 10 iterationsdid not converge in 10 iterationsdid not converge in 10 iterations
.
did not converge in 10 iterations
..
did not converge in 10 iterations
..
did not converge in 10 iterations
.
did not converge in 10 iterationsdid not converge in 10 iterationsQuick-TRANSfer stage steps exceeded maximum (= 312950)
...
did not converge in 10 iterationsdid not converge in 10 iterationsdid not converge in 10 iterations
.
did not converge in 10 iterations
....
did not converge in 10 iterationsdid not converge in 10 iterations
..
did not converge in 10 iterations
.
did not converge in 10 iterations
..
Quick-TRANSfer stage steps exceeded maximum (= 312950)did not converge in 10 iterations
.
did not converge in 10 iterationsdid not converge in 10 iterationsdid not converge in 10 iterationsdid not converge in 10 iterations
...
did not converge in 10 iterationsdid not converge in 10 iterationsdid not converge in 10 iterations
.
did not converge in 10 iterations
.
did not converge in 10 iterationsdid not converge in 10 iterationsdid not converge in 10 iterationsdid not converge in 10 iterationsdid not converge in 10 iterationsdid not converge in 10 iterations
.
did not converge in 10 iterationsdid not converge in 10 iterationsdid not converge in 10 iterations
..
did not converge in 10 iterations
...
did not converge in 10 iterations
..
did not converge in 10 iterationsdid not converge in 10 iterationsdid not converge in 10 iterationsdid not converge in 10 iterations
.
Quick-TRANSfer stage steps exceeded maximum (= 312950)did not converge in 10 iterations
.
did not converge in 10 iterationsdid not converge in 10 iterations
.
did not converge in 10 iterationsdid not converge in 10 iterations
.
did not converge in 10 iterations
..
did not converge in 10 iterations
.
did not converge in 10 iterations
.. 100 

We will choose 7 it is in the middle and look also good in the Silhouette method

cluster_computer <- kmeans(computer_scale, centers = 7, nstart = 25)
cluster_computer
K-means clustering with 7 clusters of sizes 1443, 315, 745, 2007, 316, 612, 821

Cluster means:
           hd         ram
1  0.28448917 -0.05095751
2  2.09939430  0.69997432
3 -0.48509991 -0.05095751
4 -0.91618122 -0.83102298
5  2.53457219  2.84885195
6 -0.08251343 -0.76129843
7  0.46031848  1.36972433

Clustering vector:
   1499:1    1795:2    1595:3    1849:4    3295:5    3695:6    1720:7    1995:8    2225:9   2575:10 
        4         4         4         3         7         7         4         4         3         4 
  2195:11   2605:12   2045:13   2295:14   2699:15   2225:16   1595:17   2325:18   2095:19   4395:20 
        3         3         4         3         3         4         4         4         4         1 
  1695:21   2795:22   2895:23   2875:24   4195:25   1290:26   1975:27   3995:28   3095:29   3244:30 
        4         4         7         4         1         4         4         1         7         3 
  1920:31   1995:32   2595:33   2475:34   1999:35   2675:36   2325:37   3795:38   2405:39   2425:40 
        4         4         3         4         4         4         3         1         3         3 
  2895:41   3895:42   2499:43   2255:44   3495:45   2695:46   2195:47   1749:48   2399:49   1995:50 
        3         1         3         3         7         3         4         4         4         4 
  2499:51   2395:52   2995:53   2190:54   2199:55   2125:56   2045:57   3075:58   2945:59   1945:60 
        4         4         3         4         3         4         4         4         3         4 
  3990:61   1795:62   2495:63   2220:64   2195:65   1495:66   2325:67   1499:68   2199:69   3095:70 
        3         4         3         4         4         4         4         4         4         3 
  4020:71   2725:72   1695:73   3044:74   2999:75   2844:76   1975:77   3220:78   2595:79   1629:80 
        1         4         4         3         4         3         3         3         4         3 
  3399:81   2495:82   2990:83   2720:84   2595:85   1999:86   2075:87   1795:88   1395:89   3490:90 
        4         3         3         3         3         3         3         4         4         3 
  2975:91   2145:92   2420:93   2505:94   2995:95   1495:96   1999:97   1920:98   2595:99  1695:100 
        4         4         3         3         7         4         4         4         7         4 
 1995:101  2195:102  1795:103  2999:104  1395:105  2995:106  2699:107  1720:108  2045:109  2145:110 
        4         3         4         6         4         3         3         4         4         4 
 2995:111  2095:112  3895:113  2895:114  1499:115  3165:116  2525:117  2325:118  2499:119  2799:120 
        3         4         1         7         4         4         4         3         4         4 
 1795:121  2199:122  2355:123  3220:124  2420:125  2544:126  2945:127  2295:128  1495:129  2065:130 
        4         4         3         3         3         3         4         3         4         4 
 2295:131  1799:132  2220:133  2075:134  1749:135  2195:136  2255:137  2395:138  2720:139  2195:140 
        4         4         4         4         4         3         3         4         3         4 
 2225:141  4020:142  2475:143  1975:144  3995:145  2595:146  2295:147  2199:148  1975:149  3895:150 
        3         1         3         4         1         3         4         4         3         1 
 2095:151  2225:152  3599:153  2075:154  2499:155  2575:156  2999:157  2195:158  3065:159  3399:160 
        4         3         3         3         3         3         4         3         4         4 
 1995:161  1595:162  2645:163  2345:164  2795:165  1895:166  2495:167  2599:168  1595:169  1999:170 
        4         4         4         3         7         4         3         4         4         3 
 2425:171  2495:172  1795:173  2744:174  3795:175  2745:176  2399:177  2645:178  1945:179  1695:180 
        3         3         4         3         1         4         4         3         4         4 
 2195:181  2815:182  1899:183  2644:184  3795:185  2395:186  1695:187  2575:188  2695:189  2999:190 
        4         4         4         3         1         3         4         3         7         7 
 1899:191  2499:192  1999:193  2055:194  2065:195  2055:196  2099:197  1995:198  2220:199  3220:200 
        4         4         3         4         4         3         4         4         4         3 
 3995:201  2785:202  2475:203  1499:204  1595:205  2099:206  2885:207  3795:208  2295:209  3895:210 
        1         3         3         4         4         4         3         1         4         1 
 2395:211  3135:212  2420:213  2125:214  2985:215  1395:216  2295:217  2095:218  2795:219  1945:220 
        3         3         3         4         3         4         3         4         7         4 
 2635:221  2695:222  2199:223  3895:224  2599:225  2745:226  1920:227  2895:228  2199:229  2915:230 
        3         3         3         1         3         3         4         7         4         3 
 1999:231  2720:232  1999:233  2195:234  2195:235  2295:236  1595:237  1695:238  1495:239  3795:240 
        3         3         4         3         3         4         4         4         4         1 
 1699:241  1895:242  2335:243  2495:244  2575:245  2495:246  3299:247  2699:248  1695:249  2999:250 
        4         4         3         3         3         3         7         3         4         4 
 2399:251  1499:252  2395:253  1720:254  1495:255  2399:256  3035:257  2449:258  1775:259  2599:260 
        3         4         3         4         4         4         3         4         4         7 
 2995:261  2345:262  2535:263  2345:264  1899:265  2195:266  2645:267  2785:268  2799:269  2999:270 
        3         3         3         3         4         4         3         3         7         6 
 2095:271  4020:272  2595:273  2695:274  2195:275  2995:276  2195:277  2399:278  2405:279  1795:280 
        4         1         3         7         3         7         4         3         3         4 
 2225:281  1995:282  2299:283  1795:284  2545:285  2595:286  1399:287  2475:288  2595:289  1695:290 
        3         4         4         4         3         3         4         3         7         4 
 3995:291  2999:292  2495:293  2455:294  2299:295  2690:296  2155:297  2890:298  1899:299  1595:300 
        1         4         3         3         4         7         3         7         4         4 
 1990:301  1895:302  1895:303  2799:304  2590:305  1499:306  2955:307  2285:308  2475:309  3795:310 
        4         4         4         7         3         4         3         3         3         1 
 1999:311  2599:312  2895:313  3895:314  2695:315  1995:316  2399:317  2605:318  2335:319  2195:320 
        3         3         7         1         3         4         4         3         3         4 
 2425:321  2995:322  2599:323  2390:324  1690:325  1495:326  2395:327  2099:328  3090:329  2599:330 
        3         7         7         3         4         4         3         4         7         4 
 1999:331  2195:332  2190:333  2025:334  1699:335  2790:336  1795:337  2990:338  2905:339  2825:340 
        4         4         4         4         4         7         4         7         3         3 
 2390:341  2699:342  2995:343  1590:344  2345:345  2199:346  2290:347  2595:348  2515:349  2145:350 
        4         3         3         4         3         3         4         3         3         4 
 2405:351  2525:352  2595:353  2090:354  2075:355  2799:356  3299:357  2645:358  3125:359  2295:360 
        3         3         3         4         4         4         7         3         3         3 
 1775:361  2095:362  2155:363  3075:364  2815:365  1599:366  2099:367  2645:368  1795:369  2035:370 
        4         4         3         3         3         4         4         3         4         3 
 2490:371  3225:372  2690:373  2195:374  1890:375  1995:376  2695:377  2595:378  1595:379  1490:380 
        3         4         3         3         4         4         7         7         4         4 
 2125:381  2399:382  2795:383  2290:384  2395:385  2399:386  1790:387  2099:388  1395:389  1895:390 
        3         3         7         3         3         3         4         4         4         4 
 2295:391  2595:392  1899:393  1399:394  2999:395  2999:396  2449:397  1795:398  1899:399  2395:400 
        4         3         4         4         4         7         4         4         4         3 
 2399:401  1595:402  2490:403  2995:404  2890:405  2190:406  2399:407  2285:408  2590:409  2795:410 
        3         4         3         7         7         4         3         3         3         7 
 1495:411  2075:412  2090:413  2195:414  3999:415  1699:416  1995:417  1690:418  3495:419  2195:420 
        4         4         4         3         7         4         3         4         1         4 
 3090:421  2690:422  1895:423  2495:424  2405:425  1595:426  2890:427  2390:428  1690:429  2295:430 
        7         7         4         3         3         4         7         3         4         3 
 2790:431  2695:432  2595:433  1995:434  2049:435  1399:436  2805:437  2019:438  3055:439  2990:440 
        7         7         7         4         6         4         3         4         3         7 
 2605:441  2125:442  1490:443  1699:444  2495:445  2599:446  2220:447  1590:448  1499:449  2625:450 
        3         3         4         4         3         7         3         4         4         3 
 1395:451  2395:452  2420:453  2425:454  2515:455  2375:456  3105:457  2390:458  2905:459  2690:460 
        4         3         3         3         3         3         3         4         3         7 
 2695:461  1790:462  3495:463  2790:464  1790:465  1795:466  2995:467  1995:468  2599:469  3720:470 
        3         4         1         7         4         4         3         4         1         1 
 2155:471  1599:472  2525:473  2299:474  1895:475  1490:476  2035:477  1720:478  2595:479  2290:480 
        3         4         3         1         4         4         3         4         3         4 
 2455:481  1695:482  2249:483  1999:484  2455:485  2595:486  2859:487  2599:488  2855:489  2790:490 
        3         4         4         4         3         3         4         6         3         3 
 3990:491  3595:492  2195:493  3599:494  2690:495  1999:496  2990:497  1890:498  2190:499  2720:500 
        2         1         4         1         3         3         7         4         4         3 
 2145:501  2295:502  1990:503  2695:504  3149:505  1775:506  2490:507  3599:508  2690:509  3195:510 
        4         4         4         3         3         4         3         7         3         1 
 3695:511  2645:512  3090:513  1890:514  1999:515  2935:516  1990:517  2290:518  2390:519  2025:520 
        1         3         7         4         4         3         4         4         4         4 
 2095:521  2590:522  1499:523  2325:524  2099:525  2999:526  2790:527  1590:528  2499:529  2575:530 
        4         3         4         3         4         7         3         4         4         3 
 2390:531  1495:532  2895:533  2335:534  2090:535  2815:536  2195:537  1899:538  3599:539  2095:540 
        3         4         7         3         4         3         4         4         1         4 
 2690:541  2795:542  2799:543  2698:544  2390:545  2695:546  2095:547  2599:548  1825:549  1790:550 
        7         3         4         3         3         3         4         1         4         4 
 2720:551  1295:552  2990:553  1890:554  2595:555  1490:556  2075:557  3699:558  2690:559  2245:560 
        3         4         7         4         7         4         3         7         7         4 
 3999:561  2195:562  2999:563  1895:564  2295:565  2190:566  1690:567  1390:568  1890:569  2290:570 
        7         4         4         3         3         4         4         4         4         3 
 1720:571  2325:572  1699:573  2045:574  2299:575  2755:576  2145:577  3090:578  2790:579  2099:580 
        4         3         4         4         4         3         4         7         3         4 
 1998:581  2590:582  3365:583  2545:584  3265:585  2250:586  2890:587  1599:588  1825:589  2125:590 
        4         3         1         3         1         4         7         4         4         4 
 2245:591  1945:592  2890:593  1599:594  2295:595  1520:596  2745:597  2899:598  2390:599  1675:600 
        3         4         7         4         4         4         1         3         4         4 
 3149:601  2590:602  1999:603  2590:604  1449:605  1490:606  2299:607  1595:608  2495:609  1890:610 
        3         7         4         7         4         4         3         4         3         4 
 2995:611  3609:612  2790:613  2295:614  1799:615  3990:616  2999:617  2275:618  2290:619  1499:620 
        7         6         3         3         4         2         4         3         4         4 
 2555:621  2025:622  2299:623  1975:624  2109:625  3595:626  2595:627  2395:628  1899:629  2120:630 
        3         4         1         3         4         1         3         4         4         3 
 1790:631  1899:632  1990:633  1399:634  1898:635  1725:636  2595:637  1499:638  1990:639  2595:640 
        4         4         4         4         4         4         3         4         4         3 
 1395:641  2675:642  1899:643  2990:644  1925:645  4098:646  2895:647  2495:648  1995:649  1595:650 
        4         3         4         7         4         7         7         3         3         4 
 2195:651  2399:652  2390:653  2690:654  1690:655  2398:656  2775:657  1395:658  2520:659  2125:660 
        3         3         3         3         4         3         3         4         3         3 
 4398:661  2290:662  2489:663  2190:664  2599:665  3789:666  2699:667  2799:668  2499:669  2049:670 
        7         4         3         4         4         1         7         4         4         6 
 2575:671  2999:672  3495:673  2995:674  2275:675  2590:676  2975:677  1950:678  2599:679  1695:680 
        3         7         1         7         3         3         3         4         1         4 
 2455:681  1495:682  2290:683  3720:684  1795:685  2495:686  3565:687  2845:688  2025:689  3045:690 
        3         4         3         1         4         3         1         1         3         1 
 2299:691  2345:692  2390:693  2795:694  1390:695  1749:696  2690:697  1579:698  3098:699  1295:700 
        4         3         4         7         4         4         3         4         7         4 
 1945:701  2099:702  1999:703  3090:704  1890:705  1895:706  3398:707  1845:708  1795:709  2050:710 
        4         4         3         7         4         4         7         4         4         4 
 2495:711  2375:712  1690:713  3299:714  1995:715  1495:716  2999:717  3599:718  3295:719  3999:720 
        7         3         4         1         4         4         7         7         1         1 
 3025:721  1890:722  2648:723  2295:724  2199:725  2090:726  2075:727  2744:728  2425:729  1749:730 
        2         4         3         4         6         4         3         7         1         4 
 1899:731  1520:732  1795:733  1879:734  1590:735  1890:736  1720:737  1845:738  2495:739  3099:740 
        4         4         3         4         4         4         4         3         7         7 
 2990:741  2144:742  1890:743  1975:744  1945:745  4248:746  2244:747  2044:748  1690:749  2844:750 
        7         4         4         3         4         7         3         4         4         3 
 1749:751  2395:752  1890:753  2694:754  2465:755  1999:756  1599:757  2745:758  1595:759  1999:760 
        4         3         4         7         3         3         4         3         4         4 
 1939:761  1590:762  1695:763  3048:764  1599:765  2144:766  2744:767  1399:768  2015:769  2799:770 
        4         4         4         7         4         4         7         4         4         1 
 2095:771  2544:772  3948:773  2690:774  2699:775  2490:776  2244:777  1399:778  2795:779  3595:780 
        3         4         7         7         7         3         4         4         7         1 
 2045:781  2290:782  3090:783  2644:784  2348:785  2120:786  2494:787  2394:788  1845:789  3044:790 
        4         4         7         3         3         3         4         3         4         7 
 2195:791  2995:792  1829:793  2845:794  1395:795  3495:796  2890:797  2344:798  2944:799  2290:800 
        4         7         4         3         4         1         7         4         7         3 
 2799:801  2895:802  2599:803  3499:804  1509:805  2399:806  2290:807  2544:808  2295:809  1579:810 
        4         7         4         1         4         3         4         3         3         4 
 2495:811  1944:812  1769:813  3094:814  1849:815  1744:816  2744:817  1848:818  1644:819  2344:820 
        3         4         4         7         4         4         3         4         4         4 
 2694:821  2495:822  2945:823  2395:824  2590:825  1795:826  1559:827  2444:828  1794:829  3348:830 
        3         3         3         3         7         4         4         4         4         7 
 2999:831  2294:832  2095:833  1995:834  1769:835  2059:836  2990:837  2290:838  1299:839  2399:840 
        1         4         4         3         4         4         7         3         4         3 
 3789:841  2325:842  3495:843  2644:844  2644:845  1694:846  1990:847  2225:848  1295:849  2144:850 
        1         3         1         7         3         4         4         4         4         4 
 1499:851  2294:852  3695:853  2099:854  2794:855  2590:856  1795:857  1539:858  2090:859  2344:860 
        4         3         1         4         7         3         4         4         4         3 
 2195:861  1879:862  1975:863  2390:864  3720:865  1895:866  1999:867  2595:868  2620:869  2344:870 
        3         4         4         4         1         4         4         3         3         3 
 1990:871  2094:872  1945:873  2190:874  2299:875  2444:876  2175:877  2044:878  2244:879  2125:880 
        4         4         3         4         4         3         3         4         4         3 
 2845:881  3899:882  1649:883  2595:884  3144:885  1999:886  2899:887  3090:888  2094:889  1895:890 
        3         7         4         3         7         4         4         7         4         4 
 2999:891  2994:892  1495:893  1395:894  2675:895  2394:896  2590:897  2690:898  1990:899  2190:900 
        1         7         4         4         3         4         7         7         4         3 
 3895:901  2999:902  2890:903  1799:904  2794:905  1899:906  2190:907  1399:908  2844:909  1559:910 
        2         3         7         4         3         4         4         4         7         4 
 2995:911  2325:912  1599:913  2299:914  1865:915  1990:916  1994:917  2109:918  1948:919  1575:920 
        7         4         4         3         4         4         4         4         4         4 
 2690:921  1449:922  2690:923  1695:924  2145:925  2044:926  1895:927  2015:928  2490:929  1844:930 
        3         4         3         3         4         4         3         3         3         4 
 1049:931  2595:932  2390:933  1799:934  1744:935  2565:936  2744:937  2799:938  1994:939  1495:940 
        4         7         4         4         4         3         3         3         4         4 
 2045:941  3194:942  1499:943  2194:944  3609:945  2190:946  1745:947  2590:948  1639:949  2044:950 
        3         7         4         4         6         3         4         3         4         4 
 3244:951  3595:952  1595:953  2444:954  3144:955  2395:956  1944:957  2594:958  1895:959  3044:960 
        7         1         4         4         7         3         4         3         3         7 
 2225:961  1495:962  2799:963  1544:964  2344:965  2794:966  1399:967  2295:968  2195:969  2594:970 
        3         4         3         4         1         7         4         4         4         1 
 3299:971  2194:972  3499:973  2090:974  2695:975  2644:976  1695:977  2095:978  1594:979  1845:980 
        1         1         1         4         6         1         4         4         4         4 
 2044:981  4295:982  2795:983  2045:984  2544:985  2399:986  2225:987  1470:988  1575:989  2394:990 
        4         2         7         3         1         3         4         4         4         4 
 1795:991  1599:992  1299:993  4494:994  2744:995  2444:996  2090:997  2290:998  2469:999 1495:1000 
        4         4         4         2         7         1         1         4         3         4 
 [ reached getOption("max.print") -- omitted 5259 entries ]

Within cluster sum of squares by cluster:
[1] 125.46233 246.58534  36.02784 121.99691 189.37178  49.46172 168.14783
 (between_SS / total_SS =  92.5 %)

Available components:

[1] "cluster"      "centers"      "totss"        "withinss"     "tot.withinss" "betweenss"   
[7] "size"         "iter"         "ifault"      
tidy(cluster_computer,
     col.names = colnames(computer_scale))
glance(cluster_computer)
augment(cluster_computer, computer_scale)
max_k <- 10

k_clusters <- tibble(k = 1:max_k) %>%
  mutate(
    kclust = map(k, ~ kmeans(computer_scale, .x, nstart = 25)), 
    tidied = map(kclust, tidy),
    glanced = map(kclust, glance),
    augmented = map(kclust, augment, computer)
  )

k_clusters
clusterings <- k_clusters %>%
  unnest(glanced)

clusterings
clusterings %>% 
  unnest(cols = c(augmented)) %>%
  filter(k <= 10) %>%
 ggplot(aes(x = hd, y = ram)) +
  geom_point(aes(color = .cluster)) + 
  facet_wrap(~ k)

With 7 the clusters look ok with 10 we have clusters with only 2 points, with 2 the partition doesn’t look to logical special for the point that have a ram of 15.

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